isi-entrance 2016 Q63

isi-entrance · India · UGA 4 marks Modulus function Differentiability of functions involving modulus

Let $f(x) = a_0 + a_1 |x| + a_2 |x|^2 + a_3 |x|^3$, where $a_0, a_1, a_2, a_3$ are constants.
(A) $f(x)$ is differentiable at $x = 0$ whatever be $a_0, a_1, a_2, a_3$
(B) $f(x)$ is not differentiable at $x = 0$ whatever be $a_0, a_1, a_2, a_3$ Then
(C) $f(x)$ is differentiable at $x = 0$ only if $a_1 = 0$
(D) $f(x)$ is differentiable at $x = 0$ only if $a_1 = 0, a_3 = 0$

Let $f(x) = a_0 + a_1 |x| + a_2 |x|^2 + a_3 |x|^3$, where $a_0, a_1, a_2, a_3$ are constants.\\
(A) $f(x)$ is differentiable at $x = 0$ whatever be $a_0, a_1, a_2, a_3$\\
(B) $f(x)$ is not differentiable at $x = 0$ whatever be $a_0, a_1, a_2, a_3$\\
Then\\
(C) $f(x)$ is differentiable at $x = 0$ only if $a_1 = 0$\\
(D) $f(x)$ is differentiable at $x = 0$ only if $a_1 = 0, a_3 = 0$

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